6. Prove that if x1, x2,..., Xn are distinct points in a Hausdorff space X. Prove that there are mutually disjoint open subsets U1, U2,..., Un such that X; E U; for each i.
6. Prove that if x1, x2,..., Xn are distinct points in a Hausdorff space X. Prove that there are mutually disjoint open subsets U1, U2,..., Un such that X; E U; for each i.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![6. Prove that if x1, x2,..., Xn are distinct points in a Hausdorff space X.
Prove that there are mutually disjoint open subsets U1, U2, ...,Un such that
X; E U; for each i.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F697cf92a-b0ee-445c-a1bb-63625b05267f%2Fa836199b-be5e-4b44-9c28-6b8142527716%2Ffkj7k8e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. Prove that if x1, x2,..., Xn are distinct points in a Hausdorff space X.
Prove that there are mutually disjoint open subsets U1, U2, ...,Un such that
X; E U; for each i.
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